{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# FVM Heat Flow\n",
    "\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/examples/mesh/FVM_Heat.ipynb)\n",
    "\n",
    "This example runs a heat diffusion simulation on an unstructured mesh."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %pip install --quiet phiflow\n",
    "from phi.torch.flow import *\n",
    "# from phi.flow import *  # If JAX is not installed. You can use phi.torch or phi.tf as well.\n",
    "from tqdm.notebook import trange"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "valid = union(\n",
    "    Box(x=(0, .4), y=(.45, .55)),\n",
    "    Box(x=(.3, .7), y=(0, .1)),\n",
    "    Box(x=(.3, .7), y=(.9, 1)),\n",
    "    Box(x=(.3, .4), y=1),\n",
    "    Box(x=(.6, .7), y=1),\n",
    "    Box(x=(.6, 1), y=(.45, .55)),\n",
    ")\n",
    "mesh = geom.build_mesh(Box(x=1, y=1), x=100, y=100, obstacles=~valid)\n",
    "plot(valid, mesh)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit_compile\n",
    "def step(t, dt, conductivity=1.):\n",
    "    return diffuse.implicit(t, conductivity, dt, correct_skew=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "80df473c48424eb0bc0fc0bc6e685ca9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boundary = {'x-': 1, 'x+': ZERO_GRADIENT, 'y': ZERO_GRADIENT, 'obstacle': ZERO_GRADIENT}\n",
    "t0 = Field(mesh, tensor(0), boundary)\n",
    "t_trj = iterate(step, batch(time=100), t0, dt=.01, range=trange)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "NzcuMTAw\n",
       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x1abf441d400>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(t_trj, animate='time', frame_time=50)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "phiflow2",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
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